Abstract:
The chromatic symmetric function (CSF), introduced by Stanley in 1995, is a generalization of the chromatic polynomial which enumerates proper colorings of a graph by the multiset of colors used. An open question of Stanley asks whether the CSF distinguishes trees; this question is extremely difficult and we will not be resolving it. Instead, we study it by examining a related graph invariant, the generalized degree polynomial (GDP), introduced by Crew and proved by Aliste-Prieto et al. to be determined by the CSF. Unlike the CSF, there are many known examples of non-isomorphic trees with equal GDPs. By defining a variant of the GDP for graphs with distinguished vertices, we prove a new recurrence relation for the (ordinary) GDP, and present constructions for trees with equal GDPs which together recover almost all known examples. Our work suggests a program for attacking Stanley's question using the GDP as an intermediary.
Note: Please note the special location, Smith 205. There will be no pre-seminar. The main talk starts at 4:10.
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Meeting ID: 915 4733 5974